Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Landsat Image-Based Spatiotemporal Variation Analysis of Erosion and Deposition off the Qingshuigou of the Yellow River Delta from 1984 to 2021

Owing to climate change and human activity,the Qingshuigou of the Yellow River Delta(YRD)has undergone dynamic changes in erosion and deposition.Therefore,studying these changes is important to ensure ecological protection and sustainable development.In this study,the trend of erosion-deposition evolution in the Qingshuigou was investigated based on 38 coastline phases extracted from Landsat series images of the YRD at one-year intervals from 1984 to 2021.The periodicity of the scouring and deposition evolution was also analyzed using wavelet analysis.Results showed that the total area of the Qingshuigou was affected by deposition and erosion and that the fluctuation first increased and then decreased.The total area reached a maximum in 1993.The depositional area first increased and then decreased,whereas the overall erosion area decreased.Deposition and erosion areas showed periodic changes to some extent;however,the periodic signal intensity decreased.Furthermore,factors including channel morphological evolution and variations in water and sediment discharge affect the spatiotemporal dynamics of erosion and deposition processes.The application of nonconsistency tests finally revealed that deposition area and flushing magnitude exhibited non-stationarities,which are potentially attributed to impacts from climatic change drivers.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

A novel method for gamma spectrum analysis of low-level and intermediate-level radioactive waste

The uncertainty of nuclide libraries in the analysis of the gamma spectra of low-and intermediate-level radioactive waste(LILW)using existing methods produces unstable results.To address this problem,a novel spectral analysis method is proposed in this study.In this method,overlapping peaks are located using a continuous wavelet transform.An improved quadratic convolution method is proposed to calculate the widths of the peaks and establish a fourth-order filter model to estimate the Compton edge baseline with the overlapping peaks.Combined with the adaptive sensitive nonlinear iterative peak,this method can effectively subtracts the background.Finally,a function describing the peak shape as a filter is used to deconvolve the energy spectrum to achieve accurate qualitative and quantitative analyses of the nuclide without the aid of a nuclide library.Gamma spectrum acquisition experiments for standard point sources of Cs-137 and Eu-152,a segmented gamma scanning experiment for a 200 L standard drum,and a Monte Carlo simulation experiment for triple overlapping peaks using the closest energy of three typical LILW nuclides(Sb-125,Sb-124,and Cs-134)are conducted.The results of the experiments indicate that(1)the novel method and gamma vision(GV)with an accurate nuclide library have the same spectral analysis capability,and the peak area calculation error is less than 4%;(2)compared with the GV,the analysis results of the novel method are more stable;(3)the novel method can be applied to the activity measurement of LILW,and the error of the activity reconstruction at the equivalent radius is 2.4%;and(4)The proposed novel method can quantitatively analyze all nuclides in LILW without a nuclide library.This novel method can improve the accuracy and precision of LILW measurements,provide key technical support for the reasonable disposal of LILW,and ensure the safety of humans and the environment.

Temperature-Triggered Hardware Trojan Based Algebraic Fault Analysis of SKINNY-64-64 Lightweight Block Cipher

SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a variety of ways,but it is still difficult to achieve a precisely located fault attacks at a low cost,whereas a Hardware Trojan(HT)can realize this.Temperature,as a physical quantity incidental to the operation of a cryptographic device,is easily overlooked.In this paper,a temperature-triggered HT(THT)is designed,which,when activated,causes a specific bit of the intermediate state of the SKINNY-64-64 to be flipped.Further,in this paper,a THT-based algebraic fault analysis(THT-AFA)method is proposed.To demonstrate the effectiveness of the method,experiments on algebraic fault analysis(AFA)and THT-AFA have been carried out on SKINNY-64-64.In the THT-AFA for SKINNY-64-64,it is only required to activate the THT 3 times to obtain the master key with a 100%success rate,and the average time for the attack is 64.57 s.However,when performing AFA on this cipher,we provide a relation-ship between the number of different faults and the residual entropy of the key.In comparison,our proposed THT-AFA method has better performance in terms of attack efficiency.To the best of our knowledge,this is the first HT attack on SKINNY-64-64.

Research on Auto-detection for Remainder Particles of Aerospace Relay Based on Wavelet Analysis

Aerospace relay is one kind of electronic components which is used widely in national defense system and aerospace system. The existence of remainder particles induces the reliability declining, which has become a severe problem in the development of aerospace relay. Traditional particle impact noise detection （PIND） method for remainder detection is ineffective for small particles, due to its low precision and involvement of subjective factors. An auto-detection method for PIND output signals is proposed in this paper, which is based on direct wavelet de-noising （DWD）, cross-correlation analysis （CCA） and homo-filtering （HF）, the method enhances the affectivity of PIND test about the small particles. In the end, some practical PIND output signals are analysed, and the validity of this new method is proved.

Applications of Wavelet Analysis in Differential Propagation Phase Shift Data De-noising

Using numerical simulation data of the forward differential propagation shift （ΦDP） of polarimetric radar,the principle and performing steps of noise reduction by wavelet analysis are introduced in detail.Profiting from the multiscale analysis,various types of noises can be identified according to their characteristics in different scales,and suppressed in different resolutions by a penalty threshold strategy through which a fixed threshold value is applied,a default threshold strategy through which the threshold value is determined by the noise intensity,or a ΦDP penalty threshold strategy through which a special value is designed for ΦDP de-noising.Then,a hard-or soft-threshold function,depending on the de-noising purpose,is selected to reconstruct the signal.Combining the three noise suppression strategies and the two signal reconstruction functions,and without loss of generality,two schemes are presented to verify the de-noising effect by dbN wavelets：（1） the penalty threshold strategy with the soft threshold function scheme （PSS）; （2） the ΦDP penalty threshold strategy with the soft threshold function scheme （PPSS）.Furthermore,the wavelet de-noising is compared with the mean,median,Kalman,and finite impulse response （FIR） methods with simulation data and two actual cases.The results suggest that both of the two schemes perform well,especially when ΦDP data are simultaneously polluted by various scales and types of noises.A slight difference is that the PSS method can retain more detail,and the PPSS can smooth the signal more successfully.

Research on runoff variations based on wavelet analysis and wavelet neural network model： A case study of the Heihe River drainage basin （1944-2005）

The Heihe River drainage basin is one of the endangered ecological regions of China. The shortage of water resources is the bottleneck, which constrains the sustainable development of the region. Many scholars in China have done researches concerning this problem. Based on previous researches, this paper analyzed characteristics, tendencies, and causes of annual runoff variations in the Yingluo Gorge （1944-2005） and the Zhengyi Gorge （1954-2005）, which are the boundaries of the upper reaches, the middle reaches, and the lower reaches of the Heihe River drainage basin, by wavelet analysis, wavelet neural network model, and GIS spatial analysis. The results show that： （1） annual runoff variations of the Yingluo Gorge have principal periods of 7 years and 25 years, and its increasing rate is 1.04 m^3/s.10y; （2） annual runoff variations of the Zhengyi Gorge have principal periods of 6 years and 27 years, and its decreasing rate is 2.25 m^3/s.10y; （3） prediction results show that： during 2006-2015, annual runoff variations of the Yingluo and Zhengyi gorges have ascending tendencies, and the increasing rates are respectively 2.04 m^3/s.10y and 1.61 m^3/s.10y; （4） the increase of annual runoff in the Yingluo Gorge has causal relationship with increased temperature and precipitation in the upper reaches, and the decrease of annual runoff in the Zhengyi Gorge in the past decades was mainly caused by the increased human consumption of water resources in the middle researches. The study results will provide scientific basis for making rational use and allocation schemes of water resources in the Heihe River drainage basin.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Wavelet analysis of coastal-trapped waves along the China coast generated by winter storms in 2008

This study applies the wavelet analysis to the tidal gauge records, alongshore winds, atmospheric temperature and pressure along the China coast in winter 2008. The analysis results show three events of sea level oscillations （SLOs） on the shelf induced by winter storms. The first event occurred from January 9 to 21. The SLO periods were double-peaked at 1.6-5.3 and 7.0-16.0 d with the power densities of 0.04-0.05 and 0.10-0.15 m^2.d, respectively. The second event occurred from February 5 to 18. The SLO period was single-peaked at 2.3-3.5 d with power density of 0.03-0.04 m^2.d. The third event occurred from February 20 to March 8. The SLO periods were double- peaked at 1.5-4.3 and 6.1-8.2 d with the power densities of 0.08-0.11 and 0.02-0.08 me.d, respectively. The SLOs propagated along the coast from Zhejiang in north to Guangdong in south. The phase speeds ranged about 9-29 m/s from Kanmen to Pingtan, 5-11 m/s from Xiamen to Huizhou and 11-22 m/s from Huizhou to Shuidong. The dispersion relation of the SLOs shows their nature of coastal-trapped wave.

Wavelet Analysis and Nonparametric Test for Climate Change in Tarim River Basin of Xinjiang During 1959-2006

Using wavelet analysis,regression analysis and the Mann-Kendall test,this paper analyzed time-series(1959-2006) weather data from 23 meteorological stations in an attempt to characterize the climate change in the Tarim River Basin of Xinjiang Uygur Autonomous Region,China.Major findings are as follows:1) In the 48-year study period,average annual temperature,annual precipitation and average annual relative humidity all presented nonlinear trends.2) At the 16-year time scale,all three climate indices unanimously showed a rather flat before 1964 and a detectable pickup thereafter.At the 8-year time scale,an S-shaped nonlinear and uprising trend was revealed with slight fluctuations in the entire process for all three indices.Incidentally,they all showed similar pattern of a slight increase before 1980 and a noticeable up-swing afterwards.The 4-year time scale provided a highly fluctuating pattern of periodical oscillations and spiral increases.3) Average annual relative humidity presented a negative correlation with average annual temperature and a positive correlation with annual precipitation at each time scale,which revealed a close dynamic relationship among them at the confidence level of 0.001.4) The Mann-Kendall test at the 0.05 confidence level demonstrated that the climate warming trend,as represented by the rising average annual temperature,was remarkable,but the climate wetting trend,as indicated by the rising annual precipitation and average annual relative humidity,was not obvious.

Ultrasonic C-scan Detection for Stainless Steel Spot Welding Based on Wavelet Package Analysis

An ultrasonic test of spot welding for stainless steel is conducted. Based on wavelet packet decomposition, the ultrasonic echo signal has been analyzed deeply in time - frequency domain, which can easily distinguish the nugget from the corona bond. The 2D C-scan images produced by ultrasonic C scan which contribute to quantitatively calculate the nugget diameter for the computer are further analyzed. The spot welding nugget diameter can be automatically obtained by image enhancement, edge detection and equivalent diameter algorithm procedure. The ultrasonic detection values in this paper show good agreement with the metallographic measured values. The mean value of normal distribution curve is 0.006 67, and the standard deviation is 0.087 11. Ultrasonic C-scan test based on wavelet packet signal analysis is of high accuracy and stability.

SAR image denoising based on wavelet-fractal analysis

Wavelet-fractal based SAR （synthetic aperture radar） image processing is one of the advanced technologies in image processing. The main concept of analysis is that after wavelet transformation, multifractal spectrum of the signal is different from that of noise. This difference is used to alleviate the noise produced by SAR image.The method to denoise SAR image using the process based on wavelet-fractai analysis is discussed in detail. Essentially, the present method focuses on adjusting the Hoelder exponent α of multifractal spectrum. After simulation, α should be adjusted to 1.72-1.73. The more the value of α exceeds 1.73, the less distinctive the edges of SAR image become. According to the authors denoising is optimal at α=1.72-1.73. In other words, when α =1.72-1.73, a smooth and denoised SAR image is produced.

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

Wavelet analysis of pressure fluctuation signals in a gas-solid fluidized bed

It has been shown that much dynamic information is hidden in the pressure fluctuation signals of a gas-solid fluidized bed. Unfortunately, due to the random and capricious nature of this signal, it is hard to realize reliable analysis using traditional signal processing methods such as statistical analysis or spectral analysis, which is done in Fourier domain. Information in different frequency band can be extracted by using wavelet analysis. On the evidence of the composition of the pressure fluctuation signals, energy of low frequency (ELF) is proposed to show the transition of fluidized regimes from bubbling fluidization to turbulent fluidization. Plots are presented to describe the fluidized bed's evolution to help identify the state of different flow regimes and provide a characteristic curve to identify the fluidized status effectively and reliably.

Wavelet analysis of ultrasonic A-scan signal of solid-state welded joints

In the ultrasonic nondestructive evaluation of the quality of solid state welded joints, such as friction bonding and diffusion bonding, the main difficulty is the identification of micro defects which are most likely to emerge in the welding process. The ultrasonic echo on the screen of a commercial ultrasonic detector due to a micro defect is so weak that it is completely masked by noise, and impossible to be pointed out. In the present paper, wavelet analysis (WA) is utilized to process A scan ultrasonic signals from weak bonding defects in friction bonding joints and porosity in diffusion bonding joints. First, perception of WA for engineers is given, which demonstrates the physical mechanism of WA when applied to signal processing. From this point of view, WA can be understood easily and more thoroughly. Then the signals from welding joints are decomposed into a time scale plane by means of WA. We notice that noise and the signal echo attributed to the micro defect occupy different scales, which make it possible to enhance the signal to noise ratio of the signals by proper selection and threshold processing of the time scale components of the signals, followed by reconstruction of the processed components.

APPLICATION OF WAVELET TIME-FR EQUENCY ANALYSIS TO IDENTIFICA-TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.

Features of long-term health monitored strains of a bridge with wavelet analysis

This paper analyses the five years’ monitored strains collected from a long-term health monitoring system installed on a bridge with wavelet transform.In the analysis,the monitored strains are pre-processed,features of the monitored data are summarized briefly.The influences of the base functions on the results of wavelet analysis are studied simultaneously.The results show that the db wavelet is a good mother wavelet function in the analysis,and the order N should be larger than 20,but less than 46 in decomposing the monitored strains of the bridge.According to the strain variation features of concrete bridge,the proper decomposition level is 4 in the wavelet multi-resolution analysis.With the present method,the strains caused by random loads and daily sunlight can be accurately extracted from the monitored strains.The decomposed components of the monitored strains show that the amplitudes of the strains caused by random loads,daily sunlight,and annual temperature effect,are about 5 με,25 με,and 50 με respectively.The structural response under random load is smaller than the other parts.

MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Scale-Dependent Representations of Relief Based on Wavelet Analysis

Automatic generalization of geographic information is the core of multi_scale representation of spatial data,but the scale_dependent generalization methods are far from abundant because of its extreme complicacy.This paper puts forward a new consistency model about scale_dependent representations of relief based on wavelet analysis,and discusses the thresholds in the model so as to acquire the continual representations of relief with different details between scales.The model not only meets the need of automatic generalization but also is scale-dependent completely.Some practical examples are given.